SPEED IMPROVEMENT OF MULTIVARIATE ALGORITHMS BY THE METHOD OF POSTPONED BASIS MATRIX MULTIPLICATION .1. PRINCIPAL COMPONENT ANALYSIS

Compression is one way of making analysis of large data matrices faste r. Compression is here defined as the case when a large matrix X is re placed by a smaller coefficient matrix C. The coefficients are obtaine d by least squares fitting to some compression basis. When performing, e.g., principal component analysis (PCA) of C, the results are compar able but not equal to the results from analyzing X. In this paper we s uggest a solution to this problem by rewriting the PCA algorithm in te rms of C and the compression basis matrices. This has been accomplishe d by applying a method where speed improvement is achieved by postponi ng basis matrix calculations in key steps of the PCA algorithm. The me thod suggested can also be applied to other (but not all kinds of) mul tivariate algorithms.